📝 SummarXiv

Abstract

Understanding the function of network motifs in an attempt to gain insight into how their combinations create larger reaction networks that drive cellular functions, has been a longstanding pursuit of systems biology. One specific objective within this pursuit is understanding how individual motifs respond to pulsatile and oscillatory signals. This is especially relevant because biochemical networks are often activated by signals that, in nature, occur in the form of pulses and oscillations. A powerful analytical tool for studying such dynamics is the transfer function: a compact frequency-domain description of input-output dynamics. In this work, we derive transfer functions for a set of commonly studied network motifs and characterise their responses to pulsatile and oscillatory inputs. The novelty of this review does not lie in the introduction of new mathematical theorems or biological discoveries, but in bridging well-established frequency domain formalisms from control theory with the analysis of biochemical networks under periodic forcing. In doing so, our contributions are threefold: 1. A systematic derivation and compilation of transfer functions for common network motifs: consolidating results scattered across the literature and establishing a consistent formalism for motif-level transfer functions. 2. Contextualisation of these transfer functions within biological models: extending abstract transfer functions to concrete biological settings so that the results are readily applicable without extensive mathematical labour. 3. Resolution of ambiguity between biological and control-theoretic treatments of feedback: clarifying how feedback loops should be understood within the transfer function formalism and reconciling differences between biology literature and control-oriented literature. This is done by formalising the notion of an intrinsic transfer function.